Abstract
Coresets have emerged as a powerful tool to summarize data by selecting a small subset of the original observations while retaining most of its information. This approach has led to significant computational speedups but the performance of statistical procedures run on coresets is largely unexplored. In this work, we develop a statistical framework to study coresets and focus on the canonical task of nonparameteric density estimation. Our contributions are twofold. First, we establish the minimax rate of estimation achievable by coreset-based estimators. Second, we show that the practical coreset kernel density estimators are near-minimax optimal over a large class of Hölder-smooth densities.
Original language | English (US) |
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Pages (from-to) | 2512-2520 |
Number of pages | 9 |
Journal | Proceedings of Machine Learning Research |
Volume | 130 |
State | Published - 2021 |
Event | 24th International Conference on Artificial Intelligence and Statistics, AISTATS 2021 - Virtual, Online, United States Duration: Apr 13 2021 → Apr 15 2021 |
ASJC Scopus subject areas
- Artificial Intelligence
- Software
- Control and Systems Engineering
- Statistics and Probability